极限概念教学难点分析及其突破策略

多年来，我国不少学者就极限概念教学难的问题做了大量研究，但该问题并未得到根本解决。通过对极限概念教学进行全面系统的研究，将会发现，在我国的教材体系下，极限概念教学的最大特点是难点多而密集。具体表现在极限的精确定义被高度形式化，且逻辑结构复杂、极限精确定义种类繁多、用精确定义验证极限的证明形式独特、证明技巧性强等方面。因此，为使极限概念教学难的问题得到根本解决，需采取充分铺垫、分散难点、淡化形式、借助直观、梯式演练和因材施教等策略。

Difficulties in Teaching Concepts of Limit and Strategies for Breaking through

Many scholars have researched for decades on the difficulties in teaching limit concept .However , the difficulties have never been solved radically .By thoroughly analyzing the teaching ,this paper shows that the difficulties mainly stem from the complicated logical structure of ε-definition of limit ,the great variety of precise definitions of limit , and the unusual thinking ways and skills required in proofs . To make the teaching more effectively ,this paper suggests some teaching strategies ,such as presenting limit concepts intuitively ,dispersing the difficulties ,attacking the difficulties one by one ,step by step ,and teaching in accordance with students’ aptitude ,and so on .